{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "QAOA_Demo.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "B48YJv5c6SNC",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "%%capture\n",
        "!pip install --upgrade --quiet pip\n",
        "!pip install  --quiet cirq==0.7"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kL2C06ln6h48",
        "colab_type": "text"
      },
      "source": [
        "# QAOA Experiment\n",
        "In this experiment, you are going to implement a hardware compatible QAOA algorithm for determining the Max-Cut of the processor's hardware graph (where you assign random edge weights). You will need to:\n",
        "\n",
        "1. Define a random set of weights over the hardware graph.\n",
        "2. Construct a QAOA circuit using Cirq\n",
        "3. Calculate the expectated value of the QAOA cost function.\n",
        "4. Create an outer loop optimization to minimize your cost function.\n",
        "5. Compare cuts found from QAOA with the optimal cut."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ACqqV6tJ7xXp",
        "colab_type": "text"
      },
      "source": [
        "## 1. Defining a random set of weights over the hardware graph\n",
        "In order to make the problem easily embedable on a quantum device you are going to look at the problem of Max-Cut on the same graph that the device's qubit connectivity defines, but with random valued edge weights."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rKoMKEw46XY7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 544
        },
        "outputId": "6318619a-594f-4d80-b949-58cbeee1acb3"
      },
      "source": [
        "import cirq\n",
        "import sympy\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "working_device = cirq.google.Bristlecone\n",
        "print(working_device)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                                             (0, 5)────(0, 6)\n",
            "                                             │         │\n",
            "                                             │         │\n",
            "                                    (1, 4)───(1, 5)────(1, 6)────(1, 7)\n",
            "                                    │        │         │         │\n",
            "                                    │        │         │         │\n",
            "                           (2, 3)───(2, 4)───(2, 5)────(2, 6)────(2, 7)───(2, 8)\n",
            "                           │        │        │         │         │        │\n",
            "                           │        │        │         │         │        │\n",
            "                  (3, 2)───(3, 3)───(3, 4)───(3, 5)────(3, 6)────(3, 7)───(3, 8)───(3, 9)\n",
            "                  │        │        │        │         │         │        │        │\n",
            "                  │        │        │        │         │         │        │        │\n",
            "         (4, 1)───(4, 2)───(4, 3)───(4, 4)───(4, 5)────(4, 6)────(4, 7)───(4, 8)───(4, 9)───(4, 10)\n",
            "         │        │        │        │        │         │         │        │        │        │\n",
            "         │        │        │        │        │         │         │        │        │        │\n",
            "(5, 0)───(5, 1)───(5, 2)───(5, 3)───(5, 4)───(5, 5)────(5, 6)────(5, 7)───(5, 8)───(5, 9)───(5, 10)───(5, 11)\n",
            "         │        │        │        │        │         │         │        │        │        │\n",
            "         │        │        │        │        │         │         │        │        │        │\n",
            "         (6, 1)───(6, 2)───(6, 3)───(6, 4)───(6, 5)────(6, 6)────(6, 7)───(6, 8)───(6, 9)───(6, 10)\n",
            "                  │        │        │        │         │         │        │        │\n",
            "                  │        │        │        │         │         │        │        │\n",
            "                  (7, 2)───(7, 3)───(7, 4)───(7, 5)────(7, 6)────(7, 7)───(7, 8)───(7, 9)\n",
            "                           │        │        │         │         │        │\n",
            "                           │        │        │         │         │        │\n",
            "                           (8, 3)───(8, 4)───(8, 5)────(8, 6)────(8, 7)───(8, 8)\n",
            "                                    │        │         │         │\n",
            "                                    │        │         │         │\n",
            "                                    (9, 4)───(9, 5)────(9, 6)────(9, 7)\n",
            "                                             │         │\n",
            "                                             │         │\n",
            "                                             (10, 5)───(10, 6)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gDLrxvAle_uC",
        "colab_type": "text"
      },
      "source": [
        "Since a circuit covering the entire Bristlecone device cannot be easily simulated, a small subset of the device graph will be used instead."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XoXekxuQ8bI0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 370
        },
        "outputId": "8aa441e7-9af1-414a-ed69-c0c9e9e0df82"
      },
      "source": [
        "import networkx as nx\n",
        "\n",
        "# Identify working qubits from the device.\n",
        "device_qubits = working_device.qubits\n",
        "working_qubits = sorted(device_qubits)[:12]\n",
        "\n",
        "# Populate a networkx graph with working_qubits as nodes.\n",
        "working_graph = nx.Graph()\n",
        "for qubit in working_qubits:\n",
        "  working_graph.add_node(qubit)\n",
        "\n",
        "# Pair up all neighbors with random weights in working_graph.\n",
        "for qubit in working_qubits:\n",
        "  for neighbor in working_device.neighbors_of(qubit):\n",
        "    if neighbor in working_graph:\n",
        "      # Generate a randomly weighted edge between them. Here the weighting\n",
        "      # is a random 2 decimal floating point between 0 and 5.\n",
        "      working_graph.add_edge(\n",
        "          qubit, neighbor, weight=np.random.randint(0,500) / 100)\n",
        "\n",
        "nx.draw_circular(working_graph, node_size=1000, with_labels=True)\n",
        "plt.show()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n",
            "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
            "  if not cb.iterable(width):\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
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2gfpuRbf9aKrLAL4ALVd+hXzjItxMT0Hjuf1tniPyl0FTXQqtnmLleMrKxFfV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\n2hErL3X6SEWYHBMEPs2fQT4PmBwbxLo3iW2ccVJ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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8Tucm7os-uET",
        "colab_type": "text"
      },
      "source": [
        "## 2. Construct the QAOA circuit\n",
        "Now that you have created a Max-Cut problem graph, it's time to generate the QAOA circuit following [Farhi et al.](https://arxiv.org/abs/1411.4028). For simplicity $p=1$ is chosen."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "niH8sty--Hu0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 681
        },
        "outputId": "b46d629d-020a-40e3-b027-2c7962521e5c"
      },
      "source": [
        "from cirq.contrib.svg import SVGCircuit\n",
        "\n",
        "alpha = sympy.Symbol('alpha')\n",
        "beta = sympy.Symbol('beta')\n",
        "\n",
        "qaoa_circuit = cirq.Circuit(\n",
        "    # Prepare uniform superposition on working_qubits == working_graph.nodes\n",
        "    cirq.H.on_each(working_graph.nodes()),\n",
        "\n",
        "    # Do ZZ operations between neighbors u,v in the graph. u is a qubit v is\n",
        "    # its neighbor qubit and w is the weight between these qubits.\n",
        "    (cirq.ZZ(u, v) ** (alpha * w['weight']) for (u, v, w) in working_graph.edges(data=True)),\n",
        "\n",
        "    # Apply X operations along all nodes of the graph. Again working_graph's\n",
        "    # nodes are the working_qubits. Not here we use a moment\n",
        "    # which will force all of the gates into the same line.\n",
        "    cirq.Moment(cirq.X(qubit) ** beta for qubit in working_graph.nodes()),\n",
        "    \n",
        "    # All relevant things can be computed in computational basis.\n",
        "    (cirq.measure(qubit) for qubit in working_graph.nodes()),\n",
        ")\n",
        "SVGCircuit(qaoa_circuit)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<cirq.contrib.svg.svg.SVGCircuit at 0x7fadd136b550>"
            ],
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-zbI-2KUMU66",
        "colab_type": "text"
      },
      "source": [
        "## 3. Calculating the expected value of the QAOA cost function\n",
        "Now that you have created your parameterized QAOA circuit, you are going to need a way to calculate the expectation values of the cost function. Since the cost function is the (weighted) sum of all $ZZ$ pairs in the graph you can compute all of these values simultaneously.\n",
        "\n",
        "First you need a way to estimate the expectation value given the samples from each qubit."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IqUn4uv9_IVo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def estimate_cost(graph, samples):\n",
        "    \"\"\"Estimate the cost function of the QAOA on the given graph using the\n",
        "    provided computational basis bitstrings.\"\"\"\n",
        "    cost_value = 0.0\n",
        "\n",
        "    # Loop over edge pairs and compute contribution.\n",
        "    for u, v, w in graph.edges(data=True):\n",
        "      u_samples = samples[str(u)]\n",
        "      v_samples = samples[str(v)]\n",
        "\n",
        "      # Determine if it was a +1 or -1 eigenvalue.\n",
        "      u_signs = (-1)**u_samples\n",
        "      v_signs = (-1)**v_samples\n",
        "      term_signs = u_signs * v_signs\n",
        "\n",
        "      # Add scaled term to total cost .\n",
        "      term_val = np.mean(term_signs) * w['weight']\n",
        "      cost_value += term_val\n",
        "\n",
        "    return -cost_value"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XLO0RRZarb_a",
        "colab_type": "text"
      },
      "source": [
        "Now if you run `qaoa_circuit` with a certain set of values for your placeholders you can use `estimate_expectation` to calculate the expectation value of the cost function for the circuit:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gZmW7NkBrl5Z",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "0016097a-12bf-41f6-a203-888e041474fc"
      },
      "source": [
        "alpha_value = np.pi / 4\n",
        "beta_value = np.pi / 2\n",
        "sim = cirq.Simulator()\n",
        "sample_results = sim.sample(qaoa_circuit, params={alpha: alpha_value, beta: beta_value}, repetitions=20000)\n",
        "print(f'Alpha={alpha_value} Beta={beta_value}')\n",
        "print(f'Estimated cost: {estimate_cost(working_graph, sample_results)}')"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Alpha=0.7853981633974483 Beta=1.5707963267948966\n",
            "Estimated cost: -1.2681320000000003\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rBmCr_DCsbtf",
        "colab_type": "text"
      },
      "source": [
        "## 4. Outer loop optimization\n",
        "There are lots of different techniques to choose parameters for `qaoa_circuit`. When there are only two parameters you can keep things simple and sweep over incremental pairings using `np.linspace` and track the minimum value you've found along the way."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ma0pVZwSThQx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "grid_size = 5\n",
        "exp_values = np.empty((grid_size, grid_size))\n",
        "par_values = np.empty((grid_size, grid_size, 2))\n",
        "for i, alpha_value in enumerate(np.linspace(0, 2*np.pi, grid_size)):\n",
        "  for j, beta_value in enumerate(np.linspace(0, 2*np.pi, grid_size)):\n",
        "    samples = sim.sample(\n",
        "        qaoa_circuit,\n",
        "        params={alpha: alpha_value, beta: beta_value},\n",
        "        repetitions=20000)\n",
        "    exp_values[i][j] = estimate_cost(working_graph, samples)\n",
        "    par_values[i][j] = alpha_value, beta_value"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vp-LmYLnvkzM",
        "colab_type": "text"
      },
      "source": [
        "You can also examine the cost function values w.r.t $\\alpha$ and $\\beta$:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZdSqBSuNuckY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "outputId": "b363b2bc-599a-4afa-a8d6-3030c434473f"
      },
      "source": [
        "plt.title('Heamap of QAOA Cost Function Value')\n",
        "plt.xlabel(r'$\\alpha$')\n",
        "plt.ylabel(r'$\\beta$')\n",
        "plt.imshow(exp_values)"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fadd136c5f8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GmaU5MMwszYFhZmkODDNLc2CYWZoDw8zSHBhmlubAMLM0B4aZpTX5uyTDopXj43/urHjX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\nNAeGmaU5MMwszYFhZmkODDNL+38h5hi8Ysl9RwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BzwnTYWpuKZM",
        "colab_type": "text"
      },
      "source": [
        "## 5. Compare cuts\n",
        "Since you are going to be comparing graph cuts in `working_graph` a helper function to draw them and print their the size would be useful:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6nD1YQr39KOI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 387
        },
        "outputId": "cf04838f-47bd-4815-eb47-0401ec87ba15"
      },
      "source": [
        "def output_cut(S_partition):\n",
        "  \"\"\"Plot and output the graph cut information.\"\"\"\n",
        "\n",
        "  # Generate the colors.\n",
        "  coloring = []\n",
        "  for node in working_graph:\n",
        "    if node in S_partition:\n",
        "      coloring.append('blue')\n",
        "    else:\n",
        "      coloring.append('red')\n",
        "\n",
        "  # Get the weights\n",
        "  edges = working_graph.edges(data=True)\n",
        "  weights = [w['weight'] for (u,v, w) in edges]\n",
        "\n",
        "  nx.draw_circular(\n",
        "      working_graph,\n",
        "      node_color=coloring,\n",
        "      node_size=1000,\n",
        "      with_labels=True,\n",
        "      width=weights)\n",
        "  plt.show()\n",
        "  size = nx.cut_size(working_graph, S_partition, weight='weight')\n",
        "  print(f'Cut size:{size}')\n",
        "\n",
        "# Test with the empty S and all nodes placed in T.\n",
        "output_cut([])"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n",
            "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
            "  if not cb.iterable(width):\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3n8MD9Tm+ixeBkhLsBHCtAsUT2JPIELfzrQEUgD294M8/Fag5ssjIyMDJkyd5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\nhL9SUl0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Cut size:0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t2DOLJ_3-cJt",
        "colab_type": "text"
      },
      "source": [
        "To get cuts using the QAOA you will first need to extract the best control parameters you found during your sweep:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xg5vPCt_vIrf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "d188e767-f7f0-4b11-d23f-6b4d5d33bfa8"
      },
      "source": [
        "best_exp_index = np.unravel_index(np.argmax(exp_values), exp_values.shape)\n",
        "best_parameters = par_values[best_exp_index]\n",
        "print(f'Best control parameters:{best_parameters}')"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Best control parameters:[3.14159265 6.28318531]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IRab6h39voLn",
        "colab_type": "text"
      },
      "source": [
        "Each bitstring can be seen as a candidate cut in your graph. The qubits that measured 0 correspond to that qubit being in one cut partition and a qubit that measured to 1 corresponds to that qubit being in the other cut partition. Now that you've found good parameters for your circuit, you can just sample some bistrings, iterate over them and pick the one that gives the best cut:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_1NYplopuFzu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Number of candidate cuts to sample.\n",
        "num_cuts = 100\n",
        "candidate_cuts = sim.sample(\n",
        "    qaoa_circuit,\n",
        "    params={alpha: best_parameters[0], beta: best_parameters[1]},\n",
        "    repetitions=num_cuts)\n",
        "\n",
        "# Variables to store best cut partitions and cut size.\n",
        "best_qaoa_S_partition = set()\n",
        "best_qaoa_T_partition = set()\n",
        "best_qaoa_cut_size = -9999\n",
        "\n",
        "# Analyze each candidate cut.\n",
        "for i in range(num_cuts):\n",
        "  candidate = candidate_cuts.iloc[i]\n",
        "  one_qubits = set(candidate[candidate==1].index)\n",
        "  S_partition = set()\n",
        "  T_partition = set()\n",
        "  for node in working_graph:\n",
        "    if str(node) in one_qubits:\n",
        "      # If a one was measured add node to S partition.\n",
        "      S_partition.add(node)\n",
        "    else:\n",
        "      # Otherwise a zero was measured so add to T partition.\n",
        "      T_partition.add(node)\n",
        "\n",
        "  cut_size = nx.cut_size(\n",
        "      working_graph, S_partition, T_partition, weight='weight')\n",
        "  \n",
        "  # If you found a better cut update best_qaoa_cut variables.\n",
        "  if cut_size > best_qaoa_cut_size:\n",
        "    best_qaoa_cut_size = cut_size\n",
        "    best_qaoa_S_partition = S_partition\n",
        "    best_qaoa_T_partition = T_partition"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "auo2VuTm6haO",
        "colab_type": "text"
      },
      "source": [
        "The QAOA is known to do just a little better better than random guessing for Max-Cut on 3-regular graphs at `p=1`. You can use very similar logic to the code above, but now instead of relying on the QAOA to decied your `S_partition` and `T_partition` you can just pick then randomly:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UC5Sjgt-2tjC",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import random\n",
        "\n",
        "best_random_S_partition = set()\n",
        "best_random_T_partition = set()\n",
        "best_random_cut_size = -9999\n",
        "\n",
        "# Randomly build candidate sets.\n",
        "for i in range(num_cuts):\n",
        "  S_partition = set()\n",
        "  T_partition = set()\n",
        "  for node in working_graph:\n",
        "    if random.random() > 0.5:\n",
        "      # If we flip heads add to S.\n",
        "      S_partition.add(node)\n",
        "    else:\n",
        "      # Otherwise add to T.\n",
        "      T_partition.add(node)\n",
        "\n",
        "  cut_size = nx.cut_size(\n",
        "      working_graph, S_partition, T_partition, weight='weight')\n",
        "  \n",
        "  # If you found a better cut update best_random_cut variables.\n",
        "  if cut_size > best_random_cut_size:\n",
        "    best_random_cut_size = cut_size\n",
        "    best_random_S_partition = S_partition\n",
        "    best_random_T_partition = T_partition"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2MldXTYP8QA2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 740
        },
        "outputId": "95afd9ff-a932-47e0-bed9-bcea46160b58"
      },
      "source": [
        "print('-----QAOA-----')\n",
        "output_cut(best_qaoa_S_partition)\n",
        "\n",
        "print('-----RANDOM-----')\n",
        "output_cut(best_random_S_partition)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-----QAOA-----\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n",
            "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
            "  if not cb.iterable(width):\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RneO7cgUoLASYK7tJgRoIwCwAA93OtwCQC6AQO3YoUG2YkZaWhjNnzvAOQ1bc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\n8v8K0l+EtowAlAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Cut size:29.93\n",
            "-----RANDOM-----\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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0p/guXgSKigCmyq5RoAUCMBPAAK/y1gDyABRh61YFmo0w0tPTcfLkSd5myIq3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\nlEorGviUUkqlFQ18Siml0sr/A/DeX4SETkG+AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Cut size:32.809999999999995\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kUfMrkIV8e_Z",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}